If $x \bigtriangledown y = 4x-3y$ and $x \barwedge y = 6x+y$, find $-1 \barwedge (1 \bigtriangledown 1)$.
Answer: First, find $1 \bigtriangledown 1$ $ 1 \bigtriangledown 1 = (4)(1)-(3)(1)$ $ \hphantom{1 \bigtriangledown 1} = 1$ Now, find $-1 \barwedge 1$ $ -1 \barwedge 1 = (6)(-1)+1$ $ \hphantom{-1 \barwedge 1} = -5$.